In this separability study, we also consider a zero-mean bivariate spatio-temporal random field \(\mathbf {Z}(\mathbf {s},t) = \lbrace Z_1(\mathbf {s},t),Z_2(\mathbf {s},t)\rbrace {^\top }\)  for \(t \in \lbrace 1,2, \ldots , l\rbrace \)  and \(\mathbf {s}\in \lbrace 0,1/(m-1),\ldots ,(m-2)/(m-1),1\rbrace \times \lbrace 0,1/(m-1),\ldots ,(m-2)/(m-1),1\rbrace \) . Following the way of building covariance models through latent dimensions by [1]} or using products of nonseparable functions by [2]}, we use a valid covariance function as used in Model REF .
